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Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint  [PDF]
Alexandre Scott, Francois Watier
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.312A278

We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.

Switch-When-Safe Multiperiod Mean-Variance Strategies
Rene Ferland,Francois Watier
International Journal of Statistics and Probability , 2013, DOI: 10.5539/ijsp.v2n2p59
Abstract: In this work, we study the goal-achieving probabilities of a multiperiod mean-variance financial strategy under a emph{switch-when-safe} stopping time rule. This stopping time is defined as the first moment, if it occurs, where the investor's cumulative wealth, at this point, can be safely reinvested in a simple bank account in order to meet his financial objective at the end of the investment horizon.
Estimation of first passage time densities of diffusions processess through time-varying boundaries
Imene Allab,Francois Watier
Mathematics , 2013,
Abstract: In this paper, we develop a Monte Carlo based algorithm for estimating the FPT density of a time-homogeneous SDE through a time-dependent frontier. We consider Brownian bridges as well as localized Daniels curve approximations to obtain tractable estimations of the FPT probability between successive points of a simulated path of the process. Under mild assumptions, a (unique) Daniels curve local approximation can easily be obtained by explicitly solving a non-linear system of equations.
Lability of IgE Levels Early in Life
Koffi N'guessan,David Ternant,Fran?ois Labarthe,Hervé Watier
Journal of Allergy , 2011, DOI: 10.1155/2011/547389
Abstract: We report a case of a very fast and intriguing decrease in IgE concentrations after exclusion from the diet of any CM lysate in an unusual clinical presentation of cow's milk allergy in an infant. Analysis of IgE kinetics after allergen elimination suggests rapid cessation of IgE biosynthesis and a short IgE half-life. 1. Introduction An unusual clinical presentation of cow's milk allergy (CMA) in an infant gave us the opportunity to observe a very fast and intriguing decrease of IgE concentrations after allergen withdrawal, raising new questions about IgE production and metabolism in newborns and infants. 2. Case Report A 17-day-old neonate, born to atopic parents at full term, was hospitalized in the children hospital of Tours (France) for poor feeding and increasing diarrhoea for 4 days, associated with a severe metabolic acidosis, after a symptom-free interval of 2 weeks. The diarrhoea ceased soon after admission. Erythema and a pustular rash of the face as well as a “gloves and socks-” type skin rash were noted at 18 days of age, leading to the finding of very high concentrations of total IgE (1298?kIU/L) and IgE specific to cow’s milk (CM) (83?kAU/L, Phadia) (Figure 1). First-stage formula milk had been introduced on day 11 in addition to breastfeeding according to the mother, although it is possible that this had been given since birth. Although the clinical presentation was very unusual and severe [1, 2], the diagnosis of CMA was confirmed by a rapid regression of all symptoms after withdrawal of CM proteins. Seven days later, total IgE fell to 121?kIU/L and specific IgE to 1.44?kAU/L, and total IgE returned to within the normal range (10.5?kIU/L) (Figure 1) five days later. Figure 1: Evolution of total IgE (●) and CM-specific IgE (■). IgE levels were measured on D19, D26, and D31. Predicted IgE kinetics are indicated as a black bold line. Extrapolated IgE kinetics are shown as grey lines (median in bold, 5 and 95% CI as normal lines). With only two values available, calculations were not performed for specific IgE. 3. Discussion The IgE detected in the newborn had been self-produced since IgE did not cross the placenta and his mother had no CM-specific IgE (not shown). This IgE immune response thus probably reflected a rapid maturation of IgE+ B cells into plasmablasts, as recently evidenced in mice [3]. No less spectacular was the 100-fold decrease in IgE concentrations 12 days later (Figure 1), following exclusion of any CM lysate from the diet. High levels of both specific and total IgE are regularly observed in infant cow’s milk allergy [4]
Jimmy Gautier,Laurent Baly,Pier-Giorgio Zanone,Bruno Watier
Journal of Sports Science and Medicine , 2004,
Abstract: Finswimming is a sport of speed practiced on the surface or underwater, in which performance is based on whole-body oscillations. The present study investigated the undulatory motion performed by finswimmers at the surface. This study aiming to analyze the influence of the interaction of gender, practice level, and race distance on selected kinematic parameters. Six elite and six novices finswimmers equipped with joints markers (wrist, elbow, shoulder, hip, knee, and ankle) were recorded in the sagittal plane. The position of these anatomical marks was digitized at 50 Hz. An automated motion analysis software yielded velocity, vertical amplitude, frequency, and angular position. Results showed that stroke frequency decreased whereas the mean amplitude of all joints increased with increasing race distance (p < 0.01). Mean joint amplitude for the upper limbs (wrist, elbow and shoulder) was smaller for experts than for novices. Whereas that of the ankle was larger, so that the oscillation amplitude increased from shoulder to ankle. Elite male finswimmers were pitching more acutely than female. Moreover, elite male finswimmers showed a smaller knee bending than novices and than elite females (p < 0.01). This indicated that elite male finswimmers attempt to reduce drag forces thanks to a weak knee bending and a low upper limbs pitch. To sum up, gender, expertise, and race distance affect the performance and its kinematics in terms frontal drag. Expertise in finswimming requires taking advantage of the mechanical constraints pertaining to hydrodynamic constraints in order to optimize performance
Did Media Attention of the 2009 A(H1N1) Influenza Epidemic Increase Outpatient Antibiotic Use in France?: A Time-Series Analysis
Adeline Bernier, Caroline Ligier, Didier Guillemot, Laurence Watier
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0069075
Abstract: Background In France, the 2009 A(H1N1) influenza epidemic occurred between September 2009 and January 2010. Sparking widespread controversy, it was intensely reported in the media. Despite therapeutic inefficacy, antibiotic consumption and viral respiratory infections are positively correlated, particularly in France, where antibiotic overconsumption is well-known. We first determined the period when media coverage was high, and then compared, during this period, observed outpatient antibiotic consumption to estimated outpatient antibiotic consumption “without media attention”. Materials and Methods To evaluate media coverage, two online databases were consulted: Factiva and Europresse. To quantify outpatient antibiotic consumption, we used data on reimbursements of outpatient systemic antibiotics from the computerized databases of the two main National Health Insurance agencies. Influenza-like syndromes data came from the French GPs Sentinelles Network. Weekly time-series of antibiotic consumption were modeled by autoregressive moving-average models with exogenous inputs and interventions. Analyses were computed for the entire series and by age group (0–5, 6–15, 16–60, and >60 years). Results Media coverage was intense between April 2009 and January 2010. No effect on total outpatient antibiotic consumption was observed during the whole mediatic period. However, during the epidemic in France (September 2009-January 2010), we found an antibiotic underconsumption for the entire series, 0–5 and >60 years. Additionally, at the beginning of the pandemic, when cases were still outside France (June 2009-August 2009), we found an antibiotic overconsumption for patients >16 years. Conclusion The early period of A(H1N1) virus circulation compared with seasonal influenza or an overdeclaration of ILS cases might explain the antibiotic underconsumption observed during the period of active A(H1N1) virus transmission in France. At the pandemic onset, when uncertainty was high, the overconsumption observed for individuals >16 years might have been caused by alarmist media reporting. Additional analyses are needed to understand the determinants of antibiotic consumption during this period.
The Mathematical Foundations of General Relativity Revisited  [PDF]
Jean-Francois Pommaret
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.48A022

The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy

The Mathematical Foundations of Gauge Theory Revisited  [PDF]
Jean-Francois Pommaret
Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.55026

We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using the same group theoretical methods) and the well known couplings existing between elasticity and electromagnetism (piezzo electricity, photo elasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new mathematical methods coming from the formal theory of systems of partial differential equations and Lie pseudo groups. These results finally allow unifying the previous independent tentatives done by the brothers E. and F. Cosserat in 1909 for elasticity or H. Weyl in 1918 for electromagnetism by using respectively the group of rigid motions of space or the conformal group of space-time. Meanwhile we explain why the Poincaré duality scheme existing between geometry and physics has to do with homological algebra and algebraic analysis. We insist on the fact that these results could not have been obtained before 1975 as the corresponding tools were not known before.

A Multinomial Theorem for Hermite Polynomials and Financial Applications  [PDF]
Francois Buet-Golfouse
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.66094
Abstract: Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical methods which are computationally less cumbersome than a full-fledged Monte Carlo framework, both for pricing and risk management purposes. In this paper, we review key properties of Hermite polynomials before moving on to a multinomial expansion formula for Hermite polynomials, which is proved using basic methods and corrects a formulation that appeared before in the financial literature. We then use it to give a trivial proof of the Mehler formula. Finally, we apply it to no arbitrage pricing in a multi-factor model and determine the empirical futures price law of any linear combination of the underlying factors.
The Projective Group as a Topological Manifold  [PDF]
Jean-Francois Niglio
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2018, DOI: 10.4236/alamt.2018.84012
Abstract: In this article, we start by a review of the circle group?\"\" [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle \"\". Using points on?\"\" under the complex exponential map, we can construct orthogonal projection operators. We will show that under this construction, we arrive at a topological group, denoted?\"\" of projection matrices. Together with the induced topology, it will be demonstrated that?\"\" is Hausdorff and Second Countable forming a topological manifold. Moreover, I will use an example of a group action on?\"\" to generate subgroups of?\"\".
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